First-principles study of an organometallic S=1/2 kagome compound

Cu(1,3-benzenedicarboxylate) [Cu(1,3-bdc)] contains structurally perfect kagom\'{e} planes formed by Cu$^{2+}$ ions without the presence of diamagnetic defects. This organometallic compound should have served as a precious platform to explore quantum frustrated magnetism, yet the experimental results so far are mysterious, leading to questions such as "Is Cu(1,3-bdc) just a trivial weak ferromagnet?". Using the the density functional theory, we have systematically studied the electronic and magnetic properties of Cu(1,3-bdc), putting forth a theoretical basis to clarify this novel material. We present numerical evidences of a dominating antiferromagnetic (AFM) exchange between nearest-neighbor (NN) Cu$^{2+}$ as experimentally extracted from the high-temperature susceptibility data. We further show that beyond the NN AFM exchange, the additional interactions in Cu(1,3-bdc) have similar strength as those in the well-studied kagom\'{e} antiferromagnet, Herbertsmithite, by designing a comparative study. In the end, the origin of the phase transition and FM signals observed under low temperature is discussed based on the DFT results.